# Topological Structures of Generalized Volterra-Type Integral Operators

Topological Structures of Generalized Volterra-Type Integral Operators We study the generalized Volterra-type integral and composition operators acting on the classical Fock spaces. We first characterize various properties of the operators in terms of growth and integrability conditions which are simpler to apply than those already known Berezin type characterizations. Then, we apply these conditions to study the compact and Schatten $$\mathcal {S}_p$$ S p class difference topological structures of the space of the operators. In particular, we proved that the difference of two Volterra-type integral operators is compact if and only if both are compact. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mediterranean Journal of Mathematics Springer Journals

# Topological Structures of Generalized Volterra-Type Integral Operators

, Volume 15 (2) – Feb 22, 2018
16 pages

/lp/springer_journal/topological-structures-of-generalized-volterra-type-integral-operators-dRpxa27TdQ
Publisher
Springer International Publishing
Copyright © 2018 by Springer International Publishing AG, part of Springer Nature
Subject
Mathematics; Mathematics, general
ISSN
1660-5446
eISSN
1660-5454
D.O.I.
10.1007/s00009-018-1080-5
Publisher site
See Article on Publisher Site

### Abstract

We study the generalized Volterra-type integral and composition operators acting on the classical Fock spaces. We first characterize various properties of the operators in terms of growth and integrability conditions which are simpler to apply than those already known Berezin type characterizations. Then, we apply these conditions to study the compact and Schatten $$\mathcal {S}_p$$ S p class difference topological structures of the space of the operators. In particular, we proved that the difference of two Volterra-type integral operators is compact if and only if both are compact.

### Journal

Mediterranean Journal of MathematicsSpringer Journals

Published: Feb 22, 2018

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